wiz-icon
MyQuestionIcon
MyQuestionIcon
20
You visited us 20 times! Enjoying our articles? Unlock Full Access!
Question

a and b are two vectors such that |a|=1, |b|=4, |c|2=192 and a.b=2. If c=(2a×b)3b, then the angle between b and c is

A
π3
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
π6
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
3π4
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
5π6
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is D 5π6
|a|=1, |b|=4, ab=2
c=(2a×b)3b
c+3b=2a×b

ab=2
|a||b|cosθ=2
cosθ=2|a||b|=24=12
θ=π3

|c+3b|2=|2a×b|2
|c|2+9|b|2+2c3b=4|a|2|b|2sin2θ
|c|2+9|b|2+6bc=48
|c|2+96+6(bc)=0 [1]
c=2a×b3b
bc=03×16=48

Putting value of bc in [1], we have
|c|2+966×48=0|c|=83
Putting this value in [1], we get
192+96+6|b||c|cosα=0
cosα=32
or, α=5π6

flag
Suggest Corrections
thumbs-up
1
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Vector Product
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon